Geography Reference
In-Depth Information
33
40
43
22
8
14
4
11
23
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14
8
24
34
15
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11
34
13
7
15
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14
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34
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43
26
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32
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51
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0
25 units
Figure 4.4
Moving window centred on one point: radius of 25 units.
the mean average can be given as follows, for a moving window which is a circle with
a radius of 25 units (e.g. metres):
1.
Go to location
i
.
Calculate the mean average of all values around location
2.
i
that fall within 25 m
of that location.
Make
3.
i
=
i
+ 1 (the next location is ot en at some i xed distance away and in a
predetermined direction; the locations may be nodes of a regular grid) and go
to step 1.
In Figure 4.4, a window with a radius of 25 units is centred on one observation. h e
window could be centred anywhere in the study region—the location of an observa-
tion or elsewhere. In this case, the window contains 20 values and the sum of these
values is 381. h e mean of these values is
381
/
20
= 19.05. h e approach is straightfor-
ward to apply whether the data are regularly spaced (like a grid) or irregularly spaced
(like, for example, rain gauges tend to be).
Moving windows are used widely in image processing. Usually each cell in an image
(raster grid) is visited in turn and some statistic is computed using that cell and its
immediate neighbours (note that this is termed a 'focal operator, as described in
Sections 10.3 and 10.4). h e mean in a moving window might be used to smooth an
image (reduce the ef ect of local outliers) or the standard deviation in a moving win-
dow could be used to highlight the edges of features in an image. A focal operator is
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